"The Taliban recent advances are even more significant and are as a result of an intensified military campaign; more than 50 of Afghanistan's 370 districts have fallen since the beginning of May," Lyons told the UN Security Council on Tuesday.
"Most districts have been that have been taken surround provincial capitals, suggesting that the Taliban are positioning themselves to try and take these capitals once foreign forces are fully withdrawn," Lyons continued.
The news came as a local power company told media Tuesday that violent clashes had damaged key electrical infrastructure, causing power outages in 11 provinces including Kabul.
Over the past 24 hours, Taliban fighters have taken control of several districts in Kunduz province and the important border crossing with Tajikistan, according to a Rabani Rabani, a member of the Kunduz provincial council.
The districts include Chahar Dara, Khan Abad, Imam Sahib, and as well as Shirkhan Bandar, a crossing point with Tajikistan, Rabani said.
One of them, the Chahar Dara district, fell without a fight in order to prevent civilians casualties, Rabani added.
The latest Taliban gains are in areas not traditionally under their control.
Over the weekend, the Taliban claimed it had overrun an Afghan Army base in Balkh governorate in the north of the country. A Taliban propaganda video shows the group of militants inside a military base confiscating military vehicles and weapons.
They claimed in another video that they had taken control of Afghanistan National Army Humvees in Takhar province, in the northeast.
The group also claimed in another propaganda video that dozens of Afghan forces surrendered to Taliban in Faryab province in the north of the country.
Afghan security officials could not confirm or deny these claims to CNN, and CNN cannot verify the authenticity of the videos or the date they were filmed.
In April, US President Joe Biden formally announced his decision to end America's longest war, deeming the prolonged and intractable conflict in Afghanistan no longer in alignment with American priorities.
Biden said he would withdraw US troops from Afghanistan before September 11, the 20th anniversary of the terrorist attacks that catalyzed the war on terror.
Those origins had long given way to other objectives, and Biden declared that no amount of time or money could solve the problems his three predecessors had tried and failed to fix.
Biden is planning to meet with Afghan President Ashraf Ghani and Abdullah Abdullah, the head of the country's High Council for National Reconciliation, which oversees the government's negotiation team.
"The United States will remain deeply engaged with the Government of Afghanistan to ensure the country never again becomes a safe haven for terrorist groups who pose a threat to the US homeland," White House Press Secretary Jen Psaki said Monday.
Reporting contributed by CNN's Nic Robertson in London, Mohammed Tawfeeq in Baghdad and Richard Roth in New York.